%------------------------------------------------------------------------------
% File     : GEO175+1 : TPTP v8.2.0. Released v3.3.0.
% Domain   : Geometry (Constructive)
% Problem  : Lemma on symmetry and apartness
% Version  : [vPl95] axioms : Especial.
% English  : If two lines are convergent and a point is distinct from the
%            intersection point then this point is apart from at least one of
%            these lines.

% Refs     : [vPl95] von Plato (1995), The Axioms of Constructive Geometry
%          : [ROK06] Raths et al. (2006), The ILTP Problem Library for Intu
% Source   : [ILTP]
% Names    : Lemma 4.1.ii [vPl95]

% Status   : Theorem
% Rating   : 0.00 v6.1.0, 0.04 v6.0.0, 0.50 v5.5.0, 0.12 v5.4.0, 0.17 v5.3.0, 0.26 v5.2.0, 0.14 v5.0.0, 0.05 v4.1.0, 0.06 v4.0.1, 0.05 v4.0.0, 0.10 v3.7.0, 0.00 v3.3.0
% Syntax   : Number of formulae    :   15 (   3 unt;   0 def)
%            Number of atoms       :   40 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :   32 (   7   ~;  10   |;   3   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   4 usr;   0 prp; 2-2 aty)
%            Number of functors    :    2 (   2 usr;   0 con; 2-2 aty)
%            Number of variables   :   37 (  37   !;   0   ?)
% SPC      : FOF_THM_RFO_NEQ

% Comments : Definitions unfolded, hence Especial.
%------------------------------------------------------------------------------
include('Axioms/GEO006+0.ax').
%------------------------------------------------------------------------------
fof(con,conjecture,
    ! [X,Y,U,V] :
      ( ( distinct_points(X,Y)
        & convergent_lines(U,V)
        & distinct_points(X,intersection_point(U,V)) )
     => ( apart_point_and_line(X,U)
        | apart_point_and_line(X,V) ) ) ).

%------------------------------------------------------------------------------